Expand the Trigonometric Expression (x-4)^7

${(x - 4)}^{7}$

Step 1

Use the Binomial Theorem.

$x^{7} + 7 x^{6} \cdot - 4 + 21 x^{5} {(- 4)}^{2} + 35 x^{4} {(- 4)}^{3} + 35 x^{3} {(- 4)}^{4} + 21 x^{2} {(- 4)}^{5} + 7 x {(- 4)}^{6} + {(- 4)}^{7}$

Step 2

Simplify each term.

Multiply $- 4$ by $7$ .

$x^{7} - 28 x^{6} + 21 x^{5} {(- 4)}^{2} + 35 x^{4} {(- 4)}^{3} + 35 x^{3} {(- 4)}^{4} + 21 x^{2} {(- 4)}^{5} + 7 x {(- 4)}^{6} + {(- 4)}^{7}$

Raise $- 4$ to the power of $2$ .

$x^{7} - 28 x^{6} + 21 x^{5} \cdot 16 + 35 x^{4} {(- 4)}^{3} + 35 x^{3} {(- 4)}^{4} + 21 x^{2} {(- 4)}^{5} + 7 x {(- 4)}^{6} + {(- 4)}^{7}$

Multiply $16$ by $21$ .

$x^{7} - 28 x^{6} + 336 x^{5} + 35 x^{4} {(- 4)}^{3} + 35 x^{3} {(- 4)}^{4} + 21 x^{2} {(- 4)}^{5} + 7 x {(- 4)}^{6} + {(- 4)}^{7}$

Raise $- 4$ to the power of $3$ .

$x^{7} - 28 x^{6} + 336 x^{5} + 35 x^{4} \cdot - 64 + 35 x^{3} {(- 4)}^{4} + 21 x^{2} {(- 4)}^{5} + 7 x {(- 4)}^{6} + {(- 4)}^{7}$

Multiply $- 64$ by $35$ .

$x^{7} - 28 x^{6} + 336 x^{5} - 2240 x^{4} + 35 x^{3} {(- 4)}^{4} + 21 x^{2} {(- 4)}^{5} + 7 x {(- 4)}^{6} + {(- 4)}^{7}$

Raise $- 4$ to the power of $4$ .

$x^{7} - 28 x^{6} + 336 x^{5} - 2240 x^{4} + 35 x^{3} \cdot 256 + 21 x^{2} {(- 4)}^{5} + 7 x {(- 4)}^{6} + {(- 4)}^{7}$

Multiply $256$ by $35$ .

$x^{7} - 28 x^{6} + 336 x^{5} - 2240 x^{4} + 8960 x^{3} + 21 x^{2} {(- 4)}^{5} + 7 x {(- 4)}^{6} + {(- 4)}^{7}$

Raise $- 4$ to the power of $5$ .

$x^{7} - 28 x^{6} + 336 x^{5} - 2240 x^{4} + 8960 x^{3} + 21 x^{2} \cdot - 1024 + 7 x {(- 4)}^{6} + {(- 4)}^{7}$

Multiply $- 1024$ by $21$ .

$x^{7} - 28 x^{6} + 336 x^{5} - 2240 x^{4} + 8960 x^{3} - 21504 x^{2} + 7 x {(- 4)}^{6} + {(- 4)}^{7}$

Raise $- 4$ to the power of $6$ .

$x^{7} - 28 x^{6} + 336 x^{5} - 2240 x^{4} + 8960 x^{3} - 21504 x^{2} + 7 x \cdot 4096 + {(- 4)}^{7}$

Multiply $4096$ by $7$ .

$x^{7} - 28 x^{6} + 336 x^{5} - 2240 x^{4} + 8960 x^{3} - 21504 x^{2} + 28672 x + {(- 4)}^{7}$

Raise $- 4$ to the power of $7$ .

$x^{7} - 28 x^{6} + 336 x^{5} - 2240 x^{4} + 8960 x^{3} - 21504 x^{2} + 28672 x - 16384$

Expand the Trigonometric Expression (x-4)^7

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